The twelve Imams hadith, reliable by the two parties, is reported by Al Bukhari, Muslim, and other Sunni scholars. From our side, it was also reported by Al Sheikh Al Soudduk in the Kamal Al Din book. It is reported by Jabir bin Samra, saying:
I went with my father to the prophet (pbuh), so I heard him saying:” There will appear among you twelve imams coming one after another.”. Then he said something that I didn’t hear, so I asked my father about it, so he answered: “All of them are from Quraysh”. 
This hadith is reliable also, and has no reasonable and accepted application except on the twelve Imams.
Some people tried to apply it on the rightly-guided Caliphs, on two or three persons from bani Omaya, and on two or three from bani Al Abbas.
This is a non-acceptable application where whoever reads this hadith will notice that it is an otherworldly telling from the prophet (pbuh) about an affair that has no reasonable and acceptable proof except the twelve Imam (peace be upon them).
This hadith, by commitment, indicates the birth of Al Imam Al Mahdi (pbuh) and it is assumed that Imam Al Askari died, and no one is likely to exist, so how can Imam Al Mahdi be born from a dead father? Therefore, we must assume that the birth of the Imam (pbuh) has taken place, otherwise the application of the hadith becomes invalid.
This hadith, with its own commitment, indicates the birth of the Imam (pbuh).
The third hadith that I want to mention here is Muslim’s hadith, which is reliable by the two parties, when the prophet (pbuh) says:
“One who dies without knowing the Imam of his age, will die the death of one belonging to Jahiliyyah (pre-Islamic time of ignorance)”. This hadith is also reported by Al Sunna and by Al Sheikh Al Kalini in Al Kafi book. It is reliable for both Sunni and Shiite.
Then if Al Imam Al Mahdi (ajtf) is not born now, this means that we don’t know the Imam of our period, so will die belonging to Jahiliyya.
The hadith indicates that every period of time should have an Imam, and every person is assigned to know that Imam in order not to die belonging to Al Jahiliyya. Then if Al Imam Al Mahdi is not born, how can we know the Imam of our age?
Even if these three hadiths are not applied to Al Imam Al Mahdi (pbuh), they indicate by commitment that Al Imam (pbuh) is born.
Al Imam Al Mahdi between Succession and Prospects, His Eminence Al Sheikh Mohammad Baker Al Irwani- Freely
 Kamal al-Din: 272, and Al Ghaybah by Al Tusi: 128. See Sahih Al Bukhari 9: 729, Book of Judgments, chapter on succession, and Sahih Muslim 3: 220 h 1821, Book of the Emirate, and Musnad Ahmad 5: 90.
 Kamal al-Din: 409 h 9, Al Manaqib by Ibn Shahr Ashub 3: 217, and similarly Al Kafi 1: 377 h 3, and in Musnad Al Tayalisi: 259, and Sahih Muslim 3: 239 h 1851 on the authority of Abdullah Ibn Omar: “...One who dies without having bound himself by an oath of allegiance (to an Amir), will die the death of one belonging to Jahiliyyah.”